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- Jared C. Bronski, Lincoln D. Carr, Ricardo Carretero-González, Bernard Deconinck, J. Nathan Kutz, Keith Promislow
- Physical review. E, Statistical, nonlinear, and…
- 2001

Using a standing light wave potential, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schrödinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New… (More)

- Jared C. Bronski, Lincoln D. Carr, Bernard Deconinck, J. Nathan Kutz, Keith Promislow
- Physical review. E, Statistical, nonlinear, and…
- 2001

The cubic nonlinear Schrödinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrödinger equation nor in the… (More)

- Brian G Topp, Keith Promislow, Geert J. DeVries, Robert M. Miura, Diane T. Finegood
- Journal of theoretical biology
- 2000

Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta-cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop… (More)

- Keith Promislow, Brian T. R. Wetton
- SIAM Journal of Applied Mathematics
- 2009

We present an overview of the mathematical issues that arise in the modeling of polymer electrolyte membrane fuel cells. These issues range from nanoscale modeling of network structures arising in pore formation within the polymer and the formation of nanostructured agglomerates within the catalyst layer, to macroscale models of multiphase flow and water… (More)

- Keith Promislow
- SIAM J. Math. Analysis
- 2002

We employ global quasi-steady manifolds to rigorously reduce innnite dimensional dynamical systems to nite dimensional ows. The manifolds we construct are not invariant, but through a renormalization group method we capture the long-time evolution of the full system as a ow on the manifold up to a small residual. For the parametric nonlinear Schrr odinger… (More)

The renormalization techniques for determining the long-time asymp-totics of nonlinear parabolic equations pioneered by Bricmont, Kupiainen and Lin are shown to be eeective in analyzing nonlinear wave equations featuring both dissi-pation and dispersion. These methods allow us to recover recent results of Dix in a way which is both transparent and has… (More)

A wide class of problems in the study of the spectral and orbital stability of dispersive waves in Hamiltonian systems can be reduced to understanding the so-called “energy spectrum,” that is the spectrum of the second variation of the Hamiltonian evaluated at the wave shape, which is constrained to act on a closed subspace of the underlying Hilbert space.… (More)

- Nir Gavish, Keith Promislow
- Physical review. E
- 2016

We present a microfield approach for studying the dependence of the orientational polarization of the water in aqueous electrolyte solutions upon the salt concentration and temperature. The model takes into account the orientation of the solvent dipoles due to the electric field created by ions, and the effect of thermal fluctuations. The model predicts a… (More)

- Aigen Li, Keith Promislow
- 1998

We consider the linear stability and structural stability of non-ground state traveling waves of a pair of coupled nonlinear Schrr odinger equations (CNLS) which describe the evolution of co-propagating polarized pulses in the presence of birefringence. Viewing the CNLS equations as a Hamiltonian perturbation of the Manakov equations, we nd parameter… (More)

- Andrew J. Christlieb, Jaylan Jones, Keith Promislow, Brian T. R. Wetton, Mark Willoughby
- J. Comput. Physics
- 2014